Wavelet Test of Multifractality of Asia-Pacific Index Price Series

Abstract

This paper argues for the superiority of multifractal over ARCH methods where the objective is to understand market microstructure based on accurate volatility modeling. The paper examines the multifractality of index price series on daily data of Nikkei 225, All Ordinaries, Hang Seng, KLSE Composite and Straits Times Index. Wavelets, short form waves with local support are used for time/scale decomposition of financial time series. The multifractal spectrum (MFS) of daily index prices is calculated with Wavelet Transform Modulus Maxima method described in Yalamova (2003). The MFS may reveal trading time irregularities suggested by the Multifractal Model of Asset Returns (Calvet & Fisher, 2002). The trading time deformation process may uncover information on the efficiency of the trading system that would be useful for regulatory and reorganization purposes. Multifractals describe the cascade of volatility of returns and are suited for research at different time scales simultaneously unlike ARCH type models. In addition, this method provides dimension estimates for the detection of emerging chaotic patterns. The Hurst exponent calculated from the scaling function indicates persistence in volatility of index returns. The choice of data around the October 1997 drawdown is based on the scientific evidence that markets as complex dynamical systems reveal their properties better in extreme conditions.